RE: Even if theism is a failure, it's still superior to atheism
September 21, 2022 at 7:58 am
(This post was last modified: September 21, 2022 at 8:00 am by polymath257.)
(September 20, 2022 at 8:29 pm)Jehanne Wrote:(September 20, 2022 at 6:29 pm)polymath257 Wrote: In contrast, the basic axioms of mathematics are not in doubt (outside of a few specialists). The correctness of the proof *does* say something about the truth of the conclusion.
As in finitists? (Not to derail this thread, but, it appears to be in the doghouse anyways.) Some time ago I made an edit to a Wikipedia article on finitism to point out the fact that a mathematician, a finitist, who was being cited in the present tense had, in fact, died in 1985.
Very few working mathematicians today are strict finitists, There may be a few intuitionists left, but if so they don't publish much. Debates about the Axiom of Choice are all in the past: it is accepted by the vast majority of mathematicians without comment.
In any case, all atual proofs are finite, so even a finitist would agree that a conclusion follows from some axioms, even if the axioms are not accepted.
Perhaps the biggest issue right now is in the realm of large cardinal axioms. Most set theorists accept them and most working mathematicians either don't care or are unhappy with such axioms.